Quantum algorithms for discrete spacetimes

离散时空的量子算法

• 批准号: 2882937
• 金额: --
• 依托单位: University of Edinburgh
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2882937
• 关键词: Quantum; algorithms; discrete; spacetimes

There are various indications that spacetime, fundamentally or effectively, may be discrete. These include the finiteness of black hole entropy, the discrete spectrum of the volume operator in loop quantum gravity and dualities in string theory. To capture the phenomenology of such a discrete substratum, how continuity emerges in larger scales, and where to look for predictions and new physics one needs to numerically simulate the physics on these discrete structures, especially since the randomness imposed by Lorentz invariance prohibits certain analytic approaches1. One of the greatest challenges, however, is that interesting phenomena arise in larger scales than those that are computationally tractable with classical computing. On the other hand, the mathematical formulation of spacetime as a discrete, random, partial order2, give grounds to believe that quantum algorithms could offer advantages. Specifically, there are already many quantum algorithms for graph problems offering advantage. Modifying such algorithms to deal with discrete orders is natural and at the same time novel and challenging, because of the large valence (number of nearest neighbours of an element) of the random orders that model spacetime. Moreover, the physics we will put on the computer is already discrete. Since one of the major obstacles in using quantum algorithms for physics or chemistry, is loss of accuracy and implementation cost of encoding continuous variables in the discrete variables/qubits that quantum computers use, the prospect of useful quantum advantage in a scenario where no approximation is needed is more likely.

有各种迹象表明，时空从根本上或实际上来说可能是离散的。其中包括黑洞熵的有限性、圈量子引力中体积算符的离散谱以及弦理论中的对偶性。为了捕捉这种离散基础的现象学、连续性如何在更大尺度上出现、以及在哪里寻找预测和新物理，我们需要对这些离散结构上的物理进行数值模拟，特别是因为洛伦兹不变性所施加的随机性禁止某些分析方法1。然而，最大的挑战之一是，有趣的现象会在比经典计算可处理的现象更大的范围内出现。另一方面，时空作为离散、随机、偏序的数学表述，使人们有理由相信量子算法可以提供优势。具体来说，已经有许多针对图问题的量子算法提供了优势。修改此类算法来处理离散阶是自然的，同时新颖且具有挑战性，因为模拟时空的随机阶的价数（元素的最近邻居的数量）很大。此外，我们将在计算机上呈现的物理现象已经是离散的。由于在物理或化学中使用量子算法的主要障碍之一是在量子计算机使用的离散变量/量子位中编码连续变量的准确性和实现成本的损失，因此在不需要近似的情况下更有可能发挥有用的量子优势。